Hi all, been a while since I've posted here, but figured this would be a great place to ask this question. I've gone over the first chapter of McCluney's Introduction to Radiometry a number of times, and more recently have discovered this great resource, but I am still confused about something. For the purposes of this discussion, I'm reducing the number of spatial dimensions by one. So instead of solid angle (in steradians), I'll be using angle (in radians), and instead of area (in m2), I'll be using length (in m). This is done with the full understanding that in reality, light propagates in all three spatial dimensions and intersects surfaces and not lines. Nevertheless, I believe it's useful to simplify things here. Take a look at this figure: On the left is a surface receiving light from a point source on the right. The total flux of the source is 2 pi watts, and we will assume that the angular distribution of flux is uniform, which means that the radiant intensity, as measured as exitant from the point source is uniform across all directions. Given the above, we can now say that the amount of flux contained within the depicted angle is one watt (2*pi watts divided by 2*pi radians). This means that the radiant intensity exitant from the point source is exactly one watt/radian, and this radiant intensity is the same in all directions. We can also say that the amount of flux incident upon the depicted length of the surface on the left is exactly one watt. First question: Have I got this right so far? My next question has to do with calculus, which I have a very tenuous grasp of. I understand that radiometric quantities are defined with respect to infinitesimals, and the partial, or elemental length of the surface on the left does not scale linearly with the partial angle subtended, so we can't say that the irradiance upon the surface at point P is one watt per metre. For instance, if we reduced our angle to half a radian, the length "covered" by this angle would be smaller than half a meter. Thus, as the angle gets smaller, the covered length becomes smaller at a greater rate. Thus, the flux density upon the elemental length becomes greater and greater as the angle approaches 0. Accordingly, the irradiance at point P is quite a bit greater than 1 watt/m. I lack the calculus know how to be able to figure out the derivative, but I'm guessing it has something to do with the derivative of tan theta, where theta is the angle in question. Second question: Is the above paragraph on the right track, and how would one go about figuring out the irradiance at point P that is due to the light source? Now onto the next part of my confusion. Suppose that the irradiance at point P, due to the point source, is X watts/m. Would the radiance at point P, due to the point source, be X watts/m/radian? If so, then why on earth is this a useful quantity? What does radiance tell you couldn't figure out from radiant intensity? I thought radiant intensity, irradiance, and radiance were all fundamental quantities. That to me suggests some form of independence, kind of like mass and velocity are independent properties of an object. Yet if I'm understanding this correctly, one can figure out the radiance just by knowing the radiant intensity, and the distance from an object. Why is this useful??? I remember reading something about how radiance is distance independent - i.e. the radiance of a source does not depend on the distance from the source to the target surface. I have a feeling I'm missing something ridiculously obvious, and this has been bugging me for quite a while! Finally, I kinda get that we can talk about these quantities both with respect to exitance and incidence. So in this example, assuming I was correct, the radiance at point P, due to the point source, is X watts per radian. Could we also talk about the radiance of the point source? Or could we only do that if the source of light was a surface extended in space? I'd greatly appreciate any insights here!